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A B Q Chord AB is 18. The radius of Circle Q is 15. How far is chord AB from the center of the circle? 9 15 (family!) 12 x

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A B Q Chord AB is 40, and is 15 units from the center of the circle. Find the radius of Circle Q. 20 15 (family!) 25 x

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A B Q Chord AB is 16 units from the center of circle Q. The radius of circle Q is 34. Find the length of chord AB. 34 16 (family!) x = 30 AB = 60 x

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A B Q AC = EF AB = 3x + 1 QC = 4x QF = 2x + 6 Find the radius of circle Q. 4x Because AC = EF, AB = DE. So, they are equidistant from the center 4x = 2x + 6 2x = 6 x = 3 QC = 4(3) = 12 AB = 3(3) + 1 = 10 x D C F E 2x + 6 12 5 (Family!) 13

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A B C D P E x = 20 + 64 2 x = 42˚

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A B C D P E 142 = 100 + x 2 284 = 100 + x x = 184˚

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A B C D P E (x = arc AB) 47 = 80 + x 2 94 = 80 + x x = 14˚ Arc DB = 180 – 14 = 166˚ (180 b/c AD is a diameter)

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B C D P x = 95 2 x = 47.5˚

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B C D P (x = arc CD) 33 = x 2 x = 66˚ Arcs BC and BD are congruent b/c the chords are congruent, so 360 – 66 = 294 294/2 = 147˚

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Arc BC = 360 – (76 +165) = 119

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B C D P A x = 130 - 60 2 x = 35˚

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B C D P A E 29 = x - 54 2 58 = x – 54 x = 112˚

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x = 200 – 160 2 x = 20˚ B C D P A

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B C D P A x = arc ACD Arc AD = 360 – x 85 = x – (360 – x) 2 170 = x – 360 + x 530 = 2x x = 265˚

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B C D P 120˚

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B C D P 20 The radii are 20 and 35; PB = 39. Find CD x 2 + 15 2 = 39 2 x = 36 (5, 12, 13 family) 20 15 39

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B C D P 11 The radii are 11 and 20; CD = 40. Find PB 40 2 + 9 2 = x 2 x = 41 (BTW, also a family) 11 9 40

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Circles B, C and P are tangent BC = 19 CP = 22 BP = 17 Find the radius of circle B B C P 17 – x + 19 – x = 22 -2x + 36 = 22 -2x = -14 x = 7 x x 19 - x 17 - x

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Circles B, C and P are tangent BC = 9 CP = 20 BP = 7 Find the radius of circle P B C P 7 – x + 20 – x = 9 -2x + 27 = 9 -2x = -18 x = 9 x x 20 - x 7 - x

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Tangents to Circles Pg 595. Circle the set of all points equidistant from a given point ▫Center Congruent Circles ▫have the same radius “Circle P” or.

Tangents to Circles Pg 595. Circle the set of all points equidistant from a given point ▫Center Congruent Circles ▫have the same radius “Circle P” or.

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